Significant figures and decimal places

[stoic plover]

Hi, how can I count the Significant figures and decimal places of this number?

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[stable dove]

aL

[stoic plover]

Decimal places I presume is 0 however I struggle to count significant figures

What is the definition of significant figures? My teacher didn’t include in her text

[tribal depot]

https://en.wikipedia.org/wiki/Significant_figures

[stoic plover]

I read that and I presume is 5 significant figures however I’m not sure cause I didn’t find that very clear

[tribal depot]

$$ = 454 000 $$

[stable dove]

aL

[stoic plover]

Ok but imagine the number is this but ^-7 and not ^7 . Would it be 5 significant ?

[tribal depot]

because it's 0.00....0454000...

any of the zeroes up to the first 4 are insignificant

e.g if you have 0.06, then there's one significant figure

[stoic plover]

But in this example they count the 0 in the right

[tribal depot]

yes

0.060 has two signficants

0.04540 has 4

http://www.astro.yale.edu/astro120/SigFig.pdf

very good explanation here

[stoic plover]

Ok I am going to read it. Thanks

After reading it still makes sense to me that has 5 significant figures

By this example

[tribal depot]

that is correct

note that they're all the same number

but significant figures determine the accuracy of the approximation

e.g if I tell you to give me .0454 x 10^-9 at 7 significant figures then you count the 454 as 3 and add however many zeroes at the end to get 7

[stoic plover]

I see

[stoic plover]

For counting decimal places to I.e. this I just count the ones displayed (6) and add n from x 10^-n right?

[tribal depot]

$$ 4.54 \cdot 10^{-9} $$

[stable dove]

aL

[tribal depot]

this would be 3 right?

[stoic plover]

Yes

[tribal depot]

preserve this structure

[stoic plover]

Significant figures but 2 decimal places

[tribal depot]

$$ 4.5400 \cdot 10^{-9} $$

[stable dove]

aL

[tribal depot]

5 sig figures

[stoic plover]

Yes

[tribal depot]

the number of sig figures is determined by the first term

if it was written instead 0.045400000000

then that how many sig figures it has

[stoic plover]

But now I’m talking about counting decimal places. It also varies between how we write it or we must think in the original form

[tribal depot]

you have to preserve the original form

it's 45400 in this case

however many zeroes before 4 doesn't matter

0.0000045400 for example, still 5 sig figures

[stoic plover]

So it has 0 decimal places?

Yes

[tribal depot]

decimal places is determined by the power of 10

$$ 4.54 \cdot 10^{-9}$$

[stable dove]

aL

[tribal depot]

eh nvm, you had 10^7 initially

[stoic plover]

For the number in the pic would it be 0? Because it’s an integer number

[tribal depot]

careful

1.0 is also an integer but it has 1 decimal place

[stoic plover]

Mmm ok

[tribal depot]

I'm assuming they want 4.54 x 10^5 still

[stoic plover]

However the number is 454000 and the two 0s which are significant are already in so wouldn’t it be 0?

[tribal depot]

the value of the number is 454 000

[stoic plover]

Yes

[tribal depot]

ehh, I'm actually conflicted now, I think it's zero decimal places

I don't know what you've been taught

[stoic plover]

Ok I’ll try to discuss it with other mates from my class

Thanks for the document about significant figures 🙏

[tribal depot]

[stoic plover]

Thanks @tribal depot

[unique plume]

@stoic plover has given 1 rep to @tribal depot

[deft charm]

@stoic plover

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